The field of the invention is medical imaging and particularly, methods for reconstructing images from acquired image data.
Magnetic resonance imaging (MRI) uses the nuclear magnetic resonance (NMR) phenomenon to produce images. When a substance such as human tissue is subjected to a uniform magnetic field (polarizing field B0), the individual magnetic moments of the spins in the tissue attempt to align with this polarizing field, but precess about it in random order at their characteristic Larmor frequency. If the substance, or tissue, is subjected to a magnetic field (excitation field B1) which is in the x-y plane and which is near the Larmor frequency, the net aligned moment, Mz, may be rotated, or “tipped”, into the x-y plane to produce a net transverse magnetic moment Mt. A signal is emitted by the excited spins, and after the excitation signal B1 is terminated, this signal may be received and processed to form an image.
When utilizing these signals to produce images, magnetic field gradients (Gx, Gy, and Gz) are employed. Typically, the region to be imaged is scanned by a sequence of measurement cycles in which these gradients vary according to the particular localization method being used. Each measurement is referred to in the art as a “view” and the number of views determines the quality of the image. The resulting set of received NMR signals, or views, or k-space samples, are digitized and processed to reconstruct the image using one of many well known reconstruction techniques. The total scan time is determined in part by the length of each measurement cycle, or “pulse sequence”, and in part by the number of measurement cycles, or views, that are acquired for an image. There are many clinical applications where total scan time for an image of prescribed resolution and SNR is a premium, and as a result, many improvements have been made with this objective in mind.
Projection reconstruction methods have been known since the inception of magnetic resonance imaging and this method is again being used as disclosed in U.S. Pat. No. 6,487,435. Rather than sampling k-space in a rectilinear, or Cartesian, scan pattern as is done in Fourier imaging and shown in FIG. 1, projection reconstruction methods sample k-space with a series of views that sample radial lines extending outward from the center of k-space as shown in FIG. 2. The number of views needed to sample k-space determines the length of the scan and if an insufficient number of views are acquired, streak artifacts are produced in the reconstructed image. The technique disclosed in U.S. Pat. No. 6,487,435 reduces such streaking by acquiring successive undersampled images with interleaved views and sharing peripheral k-space data between successive image frames.
Depending on the technique used, many MR scans currently used to produce medical images require many minutes to acquire the necessary data. The reduction of this scan time is an important consideration, since reduced scan time increases patient throughout, improves patient comfort, and improves image quality by reducing motion artifacts. Many different strategies have been developed to shorten the scan time.
One such strategy is referred to generally as “parallel imaging”. Parallel imaging techniques use spatial information from arrays of RF receiver coils to substitute for the encoding that would otherwise have to be obtained in a sequential fashion using RF pulses and field gradients (such as phase and frequency encoding). Each of the spatially independent receiver coils of the array carries certain spatial information and has a different sensitivity profile. This information is utilized in order to achieve a complete location encoding of the received MR signals by a combination of the simultaneously acquired data received from the separate coils. Specifically, parallel imaging techniques undersample k-space by reducing the number of acquired phase-encoded k-space sampling lines while keeping the maximal extent covered in k-space fixed. The combination of the separate MR signals produced by the separate receiver coils enables a reduction of the acquisition time required for an image (in comparison to conventional k-space data acquisition) by a factor that in the most favorable case equals the number of the receiver coils. Thus the use of multiple receiver coils acts to multiply imaging speed, without increasing gradient switching rates or RF power.
Two categories of such parallel imaging techniques that have been developed and applied to in vivo imaging are SENSE (SENSitivity Encoding) and SMASH (SiMultaneous Acquisition of Spatial Harmonics). With SENSE, the undersampled k-space data is first Fourier transformed to produce an aliased image from each coil, and then the aliased image signals are unfolded by a linear transformation of the superimposed pixel values. With SMASH, the omitted k-space lines are filled in or reconstructed prior to Fourier transformation, by constructing a weighted combination of neighboring lines acquired by the different receiver coils. SMASH requires that the spatial sensitivity of the coils be determined, and one way to do so is by “autocalibration” that entails the use of variable density k-space sampling.
A more recent advance to SMASH techniques using autocalibration is a technique known as GRAPPA (GeneRalized Autocalibrating Partially Parallel Acquisitions), introduced by Griswold et al. This technique is described in U.S. Pat. No. 6,841,998 as well as in the article titled “Generalized Autocalibrating Partially Parallel Acquisitions (GRAPPA),” by Griswold et al. and published in Magnetic Resonance in Medicine 47:1202-1210 (2002). Using these GRAPPA techniques, lines near the center of k-space are sampled at the Nyquist frequency (in comparison to the greater spaced lines at the edges of k-space). These so-called autocalibration signal (ACS) lines are then used to determine the weighting factors that are used to reconstruct the missing k-space lines. In particular, a linear combination of individual coil data is used to create the missing lines of k-space. The coefficients for the combination are determined by fitting the acquired data to the more highly sampled data near the center of k-space.
In a computed tomography (“CT”) system, an x-ray source projects a fan-shaped beam which is collimated to lie within an X-Y plane of a Cartesian coordinate system, termed the “image plane.” The x-ray beam passes through the object being imaged, such as a medical patient, and impinges upon an array of radiation detectors. The intensity of the transmitted radiation is dependent upon the attenuation of the x-ray beam by the object and each detector produces a separate electrical signal that is a measurement of the beam attenuation. The attenuation measurements from all the detectors are acquired separately to produce what is called the “transmission profile”.
The source and detector array in a conventional CT system are rotated on a gantry within the imaging plane and around the object so that the angle at which the x-ray beam intersects the object constantly changes. The transmission profile from the detector array at a given angle is referred to as a “view” and a “scan” of the object comprises a set of views made at different angular orientations during one revolution of the x-ray source and detector. In a 2D scan, data is processed to construct an image that corresponds to a two dimensional slice taken through the object.
As with MRI, there are a number of clinical applications for x-ray CT where scan time is at a premium. In time-resolved angiography, for example, a series of image frames are acquired as contrast agent flows into the region of interest. Each image is acquired as rapidly as possible to obtain a snapshot that depicts the inflow of contrast. This clinical application is particularly challenging when imaging coronary arteries or other vessels that require cardiac gating to suppress motion artifacts.
There are two methods used to reconstruct images from an acquired set of projection views as described, for example, in U.S. Pat. No. 6,710,686. In MRI the most common method is to regrid the k-space samples from their locations on the radial sampling trajectories to a Cartesian grid. The image is then reconstructed by performing a 2D or 3D Fourier transformation of the regridded k-space samples. The second method for reconstructing an MR image is to transform the radial k-space projection views to Radon space by first Fourier transforming each projection view. An image is reconstructed from these signal projections by filtering and backprojecting them into the field of view (FOV). As is well known in the art, if the acquired signal projections are insufficient in number to satisfy the Nyquist sampling theorem, streak artifacts are produced in the reconstructed image.
A new image reconstruction method called HighlY constrained backPRojection (HYPR) has been developed. As described in co-pending U.S. patent application Ser. No. 11/482,372, HYPR provides a method in which quality images can be produced with far fewer projection signal profiles when a priori knowledge of the signal information is used in the reconstruction process. For example, signal information in an angiographic study may be known to include structures such as blood vessels. That being the case, when a backprojection path passes through these structures a more accurate distribution of a signal sample in each pixel can be achieved by weighting the distribution as a function of the known signal information at that pixel location. In HYPR, for a backprojection path having N pixels the highly constrained backprojection may be expressed as follows:
            S      n        =                  (                  P          ×                      C            n                          )                              ∑                      n            =            1                    N                ⁢                  C          n                      ,
where: Sn is the backprojected signal magnitude at a pixel n in an image frame being reconstructed, P is the signal sample value in the projection profile being backprojected, and Cn is the signal value of an a priori composite image at the nth pixel along the backprojection path. The composite image is reconstructed from data acquired during the scan, and may include that used to reconstruct the given image frame as well as other acquired image data that depicts the structures in the field of view. The numerator in the equation above, (P×Cn), weights each pixel using the corresponding signal value in the composite image and the denominator,
            ∑              n        =        1            N        ⁢          C      n        ,normalizes the value so that all backprojected signal samples reflect the projection sums for the image frame and are not multiplied by the sum of the composite image.
Further, a new mathematical framework for image reconstruction termed “compressed sensing” (CS) is an emerging technique in which only a small set of linear projections of a sparse image are required to reconstruct a quality image. The theory of CS is described in E. Candès, J. Romberg, and T. Tao, “Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information,” IEEE Transactions on Information Theory 2006; 52:489-509, and D. Donoho, “Compressed sensing,” IEEE Transactions on Information Theory 2006; 52:1289-1306. The principles of CS are applicable to medical imaging and can therefore be extended to provide a general framework stating that quality medical images can be reconstructed from substantially fewer measurements than through conventional methods.